Answer:
1. A. -1.43 corresponds to an area of approximately 0.0637 under the normal curve.
B. 0.58 corresponds to an area of approximately 0.7295 under the normal curve.
C. -1.55 corresponds to an area of approximately 0.0633 under the normal curve.
D. For z>1.34, the area under the normal curve is approximately 0.0916.
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2. A. The 35th percentile corresponds to a z-score of approximately -0.48
B. The first quartile (Q1) corresponds to a z-score of approximately -0.67
C. For 12% of the data to fall above it, the z-score would be approximately 1.28
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3. A. To find the area under the curve for x< 31 inches, we need to convert 31 inches to a z-score using the formula: z = (x - mean) / standard deviation. For this case, z = (31 - 36) / 10 = -0.6, the area under the curve for this is 0.2744
B. To find the area under the curve for x> 49 inches, we need to convert 49 inches to a z-score, the z-score is (49 - 36) / 10 = 1.3, the area under the curve for this is 0.0968
C. The area under the curve for x = 40 inches is 0.3520
D. To find the height at which 70% of 5 year olds are below it, we need to use the inverse standard normal calculator, which gives us a z-score of 0.84162, we can then use this z-score to find the corresponding x value by using the formula x = mean + (z-score * standard deviation) which in this case would be 36 + (0.84162*10) = 42.4 inches